• Photonics Research
  • Vol. 9, Issue 9, 09001745 (2021)
Kai Sun1、2、†, Zi-Jian Zhang3、†, Fei Meng3、4, Bin Cheng3、5, Zhu Cao6, Jin-Shi Xu1、2、9、*, Man-Hong Yung3、7、8、10、*, Chuan-Feng Li1、2、11、*, and Guang-Can Guo1、2
Author Affiliations
  • 1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
  • 2CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
  • 3Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
  • 4Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong SAR, China
  • 5Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW 2007, Australia
  • 6Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
  • 7Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 8Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 9e-mail: jsxu@ustc.edu.cn
  • 10e-mail: yung@sustech.edu.cn
  • 11e-mail: cfli@ustc.edu.cn
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    Abstract

    The class quantum Merlin–Arthur (QMA), as the quantum analog of nondeterministic polynomial time, contains the decision problems whose YES instance can be verified efficiently with a quantum computer. The problem of deciding the group non-membership (GNM) of a group element is conjectured to be a member of QMA. Previous works on the verification of GNM, which still lacks experimental demonstration, required a quantum circuit with O(n5) group oracle calls. Here, we provide an efficient way to verify GNM problems, in which each quantum circuit only contains O(1) group of oracle calls, and the number of qubits in each circuit is reduced by half. Based on this protocol, we then experimentally demonstrate the new verification process with a four-element group in an all-optical circuit. The new protocol is validated experimentally by observing a significant completeness-soundness gap between the probabilities of accepting elements in and outside the subgroup. This work efficiently simplifies the verification of GNM and is helpful in constructing more quantum protocols based on the near-term quantum devices.
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    Kai Sun, Zi-Jian Zhang, Fei Meng, Bin Cheng, Zhu Cao, Jin-Shi Xu, Man-Hong Yung, Chuan-Feng Li, Guang-Can Guo. Experimental verification of group non-membership in optical circuits[J]. Photonics Research, 2021, 9(9): 09001745
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    Category: Quantum Optics
    Received: Apr. 16, 2021
    Accepted: Jun. 29, 2021
    Published Online: Aug. 20, 2021
    The Author Email: Jin-Shi Xu (jsxu@ustc.edu.cn), Man-Hong Yung (yung@sustech.edu.cn), Chuan-Feng Li (cfli@ustc.edu.cn)